High reduction transmissions can be realized with bevel ring gears that face each other with a shaft angle which is not equal to 180° (e.g. U.S. Pat. No. 7,147,583 to Lemanski). Such transmissions, known as pericyclic transmissions, comprise a system including a high reduction ratio, high tooth contact ratio, and nutating/rotating gear mechanism which incorporates meshing conjugate bevel ring gear or face-gear pairs. For example, the pericyclic transmission 2 shown in FIG. 1 has an input shaft 4 which is connected to a bearing 6 inclined at a nutating angle. The outer ring of the bearing is connected to the pericyclic motion converter 8 which has teeth on both faces. The number of teeth on the pericyclic motion converter 8 differs by between 1 and 4 from the number of teeth of a reaction control member 10 which is rigidly connected to the housing 12. Each rotation of the input shaft 4 will cause a nutation motion of the pericyclic motion converter 8 which is in mesh with the reaction control member 10 on the left side and an output gear 14 on the right side. The output gear 14 has the same number of teeth as the reaction control member 10.
If the number of teeth on the pericyclic motion converter 8 is, for example, 2 higher than the number of teeth of the reaction control member 10 (and the output gear 14), then each revolution of the input shaft 4 will rotate the output shaft 16 (which is rigidly connected to the output gear) by 2 pitches (i.e. 2 teeth). If the number of teeth on the output gear is, for example, 54, then the ratio of the transmission is i=360°/[(360°/54)*2]=27 (or 27×1). This shows that the principle of a nutating pericyclic motion converter can realize very high speed reductions in a very compact arrangement with a low number of rotating parts. The contact ratio between the teeth of the pericyclic motion converter 8 and the reaction control member 10 as well as the output gear 14 is very high. It is possible that 5 or more teeth participate on the motion transmission which enables the use of rather small gears for a high torque transmission. The low rotational motion of the pericyclic motion converter 8 will minimize the energy loss due to friction in the tooth meshing process and therefore results in a high transmission efficiency.
It is possible to introduce additional rotation between the housing part 12, which is rigidly connected to the reaction control member 10, and the input shaft 4. This motion can be actuated by an electric motor 18 with variable speed control which is controlled by an electronic circuitry. This addition effectively converts the high reduction transmission into an infinite variable transmission.
Transmissions as described above have not been realized as production units in real industrial applications. Only prototypes have been manufactured using machining centers with ball nose end mills which required very long machining times and served the purpose of proving the concept of this transmission principle. The following observations have been made which explain the obstacle of industrial, cost-effective manufacturing of the gears especially the pericyclic motion converter 8.
The pitch cone apexes of the reaction control member 10 and the pericyclic motion converter 8 are coincident at the intersecting point of the axis of the two gear members which is given by physical law. An arrangement of this type is shown by the gears 20, 22 of FIGS. 2(a) and 2(b). This is also true if the number of teeth of the two facing ring gear combinations are different (as in the pericyclic transmission 2). If the two facing bevel ring gears have a shaft angle between 178° and 175°, then the pitch cone can be drawn as shown in FIG. 2(b) which means the reaction control member 10 (and the output gear 14) are external ring gears and the pericyclic motion converter 8 has internal bevel gears on both faces. For the purposes of discussion, external bevel gears are considered to be those gears having pitch angles of less than 90 degrees thereby having teeth that point outward and away from the axis of the gear. Internal bevel gears are considered to be those gears having pitch angles of greater than 90 degrees thereby having teeth that point inward toward the axis of the gear.
Internal spiral bevel gears cannot be manufactured conventionally because the cutter has to approach the tooth from the back side (FIGS. 2c and 2d) of the gear and would generate the tooth instead the slot. The result would be complete destruction of the internal gear. Even if it was possible (according to bevel gear generating principles) to cut the internal gear from the front (FIG. 2c), the circular cutter path would cause secondary cuts and lead to mutilations which would destroy the teeth at the opposite side of the cutting zone (e.g. FIG. 6, interference area).
Face gear solutions as indicated in FIG. 3 where the external and the internal face gear member can be derived from the same shaper cutter have also been disclosed. FIG. 3 shows a spur gear shaper cutter in a position where it generates an external face gear tooth on the left gear and in the same position an internal face gear tooth on the right gear. It can be observed that the shaper cutter approaches the external gear from the front (external), where the same section of the shaper cutter is supposed to form the teeth of the internal gear in the same position. This results in the shaper cutter destroying and eliminating the outer rim of the internal face gear in order to reach the tooth flanks from the back side. This relationship which is required in order to generate the correct mating flank to the external face gear cannot be realized in a practical manufacturing.
The discussion above identifies some of the reasons that have prevented the conventional manufacturing of internal bevel gears. The existing prototypes have been manufactured either with three dimensional printing or with ball nose end mills on multi-axis machining centers. The machining center, for example, typically utilizes surface coordinates which can be calculated using a cutting simulation that works regardless of the fact that in actual practice, the parts would be mutilated or destroyed while cutting the slots from the back side.